Best Known (83−71, 83, s)-Nets in Base 25
(83−71, 83, 126)-Net over F25 — Constructive and digital
Digital (12, 83, 126)-net over F25, using
- t-expansion [i] based on digital (10, 83, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(83−71, 83, 1073)-Net in Base 25 — Upper bound on s
There is no (12, 83, 1074)-net in base 25, because
- 1 times m-reduction [i] would yield (12, 82, 1074)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 4 328691 698870 564521 621712 990672 604185 801456 536134 131150 997794 320368 081820 295770 224385 674589 198794 848623 692728 407633 > 2582 [i]